My solicitor keeps all the title deeds securely, i have copy deeds.
This is in Scotland, and the deeds – copies – can be ordered online from Registers of Scotland
Normally not (wasnt) recommended to have your own original copy (in case you lost them).
When pay the mortgage off, normally the solicitor clearing the charge on the property will offer to keep them in safe storage for you. Your originals with the conveyancing solicitor?
Edit to add – In Scotland. Not all deeds have been digitised and put on the Land Register, so the non digitised ones are still on the old Sasine Register – so expected to have/keep the originals for safe keeping.